A finite-element method using dispersion reduced spline elements for room acoustics simulation

Abstract

This paper presents a finite element method (FEM) using hexahedral 27-node spline acoustic elements (Spl27) with low numerical dispersion for room acoustics simulation in both the frequency and time domains, especially at higher frequencies. Dispersion error analysis in one dimension is performed to increase the accuracy of FEM using Spl27 by modifying the numerical integration points of element stiffness and mass matrices. The basic accuracy and efficiency of the FEM using the improved Spl27, which uses modified integration points, are presented through numerical experiments using benchmark problems in both the frequency and time domains, revealing that FEM using the improved Spl27 in both domains provides more accurate results than the conventional method does, and with fewer degrees of freedom. Moreover, the effectiveness of FEM using the improved Spl27 over that using hexahedral 27-node Lagrange elements is shown for time domain analysis of the sound field in a practical sized room.